Łojasiewicz inequalities in a certain class of smooth functions (Q6621127)

In this interesting paper, the authors study the Łojasiewicz inequalities for non-degenerate smooth functions, satisfying the Kamimoto and Nose condition (KN-condition). Under these conditions, a non-degenerate smooth function admits a toric resolution of singularities. The authors prove that a germ at the origin of a non-degenerate smooth function \(f: \mathbf R^n \to \mathbf R\) satisfying KN-condition admits Łojasiewicz inequalities. Furthermore, they compute the Łojasiewicz exponents in some special cases and describe classes of functions whose Łojasiewicz exponents can be expressed in a simple way in terms of their Newton polyhedron.\N\NFor the entire collection see [Zbl 1547.32001].